www.VadoseZoneJournal.org Numerical EvaluaƟon of a Sensible Heat Balance Method to Determine Rates of Soil Freezing and Thawing In situ determinaƟon of soil freezing and thawing is difficult despite its importance for many environmental processes. A sensible heat balance (SHB) method using a sequence of heat pulse probes has been shown to accurately measure water evaporaƟon in subsurface soil, and it has the potenƟal to measure soil freezing and thawing. DeterminaƟon of soil freezing and thawing may be more challenging than evaporaƟon, however, because the latent heat of fusion is smaller than the latent heat of vaporizaƟon. Furthermore, convecƟve heat flow associated with liquid water flow and occurrence of evaporaƟon or condensaƟon during freezing and thawing may cause inaccurate esƟmaƟon of freezing and thawing with the SHB method. The objecƟve of this study was to examine the applicability of the SHB concept to soil freezing and thawing. Soil freezing and thawing events were simulated with the simultaneous heat and water (SHAW) model. Ice contents were esƟmated by applying the SHB concept to numerical data produced by the SHAW model. Close agreement between the SHB-esƟmated and the SHAW-simulated ice contents were observed at depths below 24 mm. The main cause of inaccuracies with the SHB method was poor esƟmaƟon of heat conducƟon at the 12-mm depth, possibly due to simplificaƟons of temporal or ver Ɵcal distribuƟons of temperature and thermal conducƟvity. The effects of convecƟve heat flow and concurrent evaporaƟon or condensaƟon and freezing or thawing on the SHB method were small. The results indicate that the SHB method is conceptually suitable for esƟmaƟng soil freezing and thawing. Independent, accurate esƟmates of thermal proper Ɵes must be available to effecƟvely use the SHB method to determine in situ soil freezing and thawing. AbbreviaƟons: DOY, day of the year; SHAW, simultaneous heat and water; SHB, sensible heat balance. Soil freezing and thawing have criƟcal effects on water and chemical movement in the soil during winter and spring. Ice in partially frozen soil can interrupt the iniltration of rainfall or snowmelt, leading to surface runof and erosion (Kane and Stein, 1983; Cruse et al., 2001). Furthermore, frozen soils have a low matric potential similar to dry soils (Williams, 1964; Koopmans and Miller, 1966), so that liquid water low from warm layers into cold layers, generally upward in direction, is induced (Dirksen and Miller, 1966; Kung and Steenhuis, 1986). Simultaneously, liquid water low causes advective move- ment of dissolved chemicals (Cary and Mayland, 1972; Cary et al., 1979; Galinato, 1987). Liquid water moving upward into colder layers causes increasing ice content in the freezing zone. Moreover, the formation of ice lenses by freezing results in soil structural changes (Penner, 1967; Miller, 1972; Gieselman et al., 2008). Hence, determining water contents, water low rates, and water-to-ice phase changes in partially frozen soils is important. Continuous in situ measurement of unfrozen water content has been successful using dielec- tric permittivity measurements such as time-domain relectometry (TDR) (Stein and Kane, 1983; Hayhoe et al., 1983; Spaans and Baker, 1995). It has been reported that the relationship between dielectric permittivity of partially frozen soils and liquid water content is depen- dent on the total water content so that calibrations taking into account ice permittivity are required for accurate measurements (Spaans and Baker, 1995; Seyfried and Murdock, 1996; Watanabe and Wake, 2009). Temporal in situ measurements of ice formation and thawing in soil have been diicult to obtain in spite of their importance. Few studies on estimating the soil volumetric ice content have been reported. Kelleners and Norton (2012) estimated the volumetric ice content with a dielectric permittivity sensor and a dielectric mixing model (Bittelli et al., 2003). hey assumed that the total water content did not change during soil freezing. hat assumption ignores liquid water supplied from snow cover or by liquid water low in partially frozen soil. Bittelli et al. (2004) examined a mixing model used in conjunc- tion with dielectric permittivities measured at two diferent frequencies. he method was The applicability of the sensible heat balance (SHB) concept for esƟmat- ing soil freezing and thawing rates was tested in a numerical modeling study. Results indicated that the SHB method was suitable for esƟmaƟng soil freezing and thawing rates at depths below 24 mm. ApplicaƟon of the method requires accurate esƟ- mates of soil thermal proper Ɵes. Y. Kojima and R. Horton, Agronomy Dep., Iowa State Univ., Ames, IA 50011; J.L. Heitman, Soil Science Dep., North Carolina State Univ., Raleigh, NC 27695; and G.N. Flerchinger, USDA-ARS, Northwest Watershed Research center, Boise, ID 83712. *Corresponding author (ykojima@iastate.edu). Vadose Zone J. doi:10.2136/vzj2012.0053 Received 27 Apr. 2012. Special Section: Frozen Soils Yuki Kojima* Joshua L. Heitman Gerald N. Flerchinger Robert Horton © Soil Science Society of America 5585 Guilford Rd., Madison, WI 53711 USA. All rights reserved. No part of this periodical may be reproduced or transmiƩed in any form or by any means, electronic or mechanical, including pho- tocopying, recording, or any informaƟon storage and retrieval system, without permission in wriƟng from the publisher.